Issue

TROLL model currently compute leaf lifespan with Reich’s allometry (Reich et al. 1991). But we have shown that Reich’s allometry is underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometry underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.

We tested different models starting from complet model Mcomp: \[ {LL_s}_j \sim \mathcal{logN}(log({\mu_s}_j),\,\sigma)\,, ~~s=1,...,S_{=4}~, ~~j=1,...,n_s\]

\[{\mu_s}_j = {\beta_0}*e^{{\beta_1}_s*{LMA_s}_j^{{\beta_3}_s} - {\beta_2}_s*{Nmass_s}_j^{{\beta_4}_s}}\] \[{\beta_i}_s \sim \mathcal{N}({\beta_i},\,\sigma_i)\,^I\] \[(\beta_i, \sigma, \sigma_i) \sim \mathcal{\Gamma}(0.001,\,0.001)\,^{2I+1}\]

LL graph

Figure 1: Leaf mass per area (LMA), leaf nitrogen content (Nmass) and leaflifespan (LL). Leaf mass per area (LMA in \(g.m^{-2}\)), leaf nitrogen content (Nmass, in \(mg.g^-1\)) and leaf lifespan (LL in \(months\)) are taken in GLOPNET dataset from Wright et al. (2004).

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + {\beta_2}_s*N,\sigma)\,\] Maximum likekihood of 11.0675641

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -0.9630255

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + {\beta_2}_s*N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 21.0111855

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + N,\sigma)\,\] Maximum likekihood of 0.9651896

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -1.784339

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 4.3829642

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA,\sigma)\,\] Maximum likekihood of 4.215306

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of -7.1051104

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 9.2432682

Convergence

Result

\[LL = 1.353*e^{0.049 *LMA^{0.773}}\]

Figure 3: Model predictions.